The Antiresonant Reflecting Optical Waveguide Fiber Sensor

*Ran Gao and Jiansen Ye*

### **Abstract**

In this chapter, the optical fiber sensors based on antiresonant reflecting optical waveguide have been introduced, including the single layer, double layers, double resonators, and hybrid mechanism. Various optical fiber sensors based on antiresonant reflecting optical waveguide have been introduced in this chapter with different working principles, including the fiber optic vibration sensor, humidity sensor, strain sensor, temperature sensor, magnetic field sensor, biosensor, etc. Especially, many long-standing challenges in the fiber optic sensor can be solved through the working principle of the antiresonant reflecting optical waveguide, including the temperature cross-talk compensation, distribution localization, optofluidic biosensing, etc. In general, the optical fiber sensors based on antiresonant reflecting optical waveguide have advantages, such as compact structure, high sensitivity, large dynamic range, and high stability, which appear to have potential applications in researches of structure health monitoring, oil exploiting, and biology detection.

**Keywords:** antiresonant reflecting optical waveguide, Fabry-Pérot resonator, double layers, double resonators, hybrid mechanism

### **1. Background**

Over past two decades, the antiresonant reflecting optical waveguide (ARROW) has developed into a versatile platform for a range of interdisciplinary applications in low loss communication [1], ultrafast optics [2], optical amplifiers [3], and biophotonics [4]. In the ARROW, the guided light is reflected at the two surfaces of the cladding in the hollow-core fiber (HCF), forming a Fabry-Pérot etalon [5]. The guided light at the antiresonant wavelength can be propagated along the HCF. Due to the unique light guiding mechanism, the ARROW is a good candidate for the fiber optic sensor: (i) the optical properties of the ARROW can be easily manipulated with the cladding structure, making the flexibility for fiber optic sensors; (ii) the guided light can break the confining of the fiber core, forming an enhanced interaction between the light and the ambient medium; and (iii) the hollow holes in the HCF is a natural channel for the optofluidic biosensors, which reduce the complexity of the fiber optic sensor significantly. Many sensing principles of ARROWs for fiber optic sensors have been researched in recent years, including the ARROW with the single layer, double layers, double resonators, hybrid mechanism, etc. [6]. The ARROW-based fiber optic sensors possess great flexibility, high sensitivity, and low cost, which are expected to be used for many fields in real-world


The ARROW can be used to study the optical conduction mechanism of lowindex core fibers, which is similar to Fabry-Pérot resonators [6]. **Figure 1** shows the structure diagram of the ARROW, where the gray part is the high-index layer with RI n2 (silica) corresponding to the Fabry-Pérot resonator cavity and the dark gray part is the low-index layer with RI n1 (air) [17, 18]. When the wavelength of the optical fiber satisfies the resonance condition, it will leak out from the high fold rate layer corresponding to the low transmission intensity part of the transmission spectrum, which is similar to the destructive interference of light in the Fabry-Pérot cavity [19, 20]. In contrast, the light of the antiresonance wavelength will be reflected back at the interface of the high and low RIs and will be restricted to be transmitted in the fiber core. So most of the light will be reflected back to the fiber core [20]. Based on the principle of the antiresonant waveguide, the optical fiber sensor can be made into different types by changing the relevant parameters. Optical fiber sensors based on the antiresonant waveguide are mainly divided into two types [21]. The first is to change the resonant wavelength by changing the RI or the length of the Fabry-Pérot cavity. The second is to change the contrast of the output intensity of the antiresonant waveguide by changing the associated external material composition [19, 20]. The optical fiber sensor of the ARROW finally realizes the measurement of different physical quantities through these two kinds of modulation methods. This chapter will introduce the working principles of various

ARROW-based fiber optic sensors in detail [20, 21].

*The Antiresonant Reflecting Optical Waveguide Fiber Sensor*

*DOI: http://dx.doi.org/10.5772/intechopen.93345*

tion sensor [7].

**13**

**Figure 1.**

*The structure of ARROW.*

**3. The antiresonant reflecting optical waveguide sensor**

**3.1 The single-layered antiresonant reflecting optical waveguide sensor**

is the single-layered antiresonant reflecting optical waveguide (SL-ARROW), which is widely used in optical fiber sensors. The SL-ARROW mode in the capillary waveguide is sensitive to the surrounding environments, and various sensing applications have been proposed, such as vibration sensor, humidity sensor, water-level sensing, etc. The working principle of the SL-ARROW is introduced by the vibra-

Vibration signal detection is very important in the application of structural monitoring in people's life. Vibration detection can monitor the safety of building structures such as buildings, highways, bridges, dams, highways, and so on. In general, the vibration can be detected by piezoelectric, magneto-electric, and current sensors [22]. SL-ARROW is an optical fiber vibration sensor, which is designed based on the principle of antiresonant waveguide. The fiber optic sensor is a good alternative with several unique advantages such as low weight, immunity to electromagnetic interference, and long-distance signal transmission for remote

The simplest model of the antiresonant reflecting optical waveguide (ARROW)

#### **Table 1.**

*The optical fiber sensor based on ARROW [7–15].*

applications [5, 6]. The optical fiber sensor based on the principle of ARROW is mainly applied in the optical fiber vibration sensor, optical fiber humidity sensor, water-level sensor, fiber strain sensor, fiber optic magnetic field sensor, fiber optic biosensors, optical fiber pressure sensor, optical fiber temperature sensor, and other types of optical fiber sensors. The common optical fiber sensors based on the ARROW principle and their performance are shown in **Table 1**.

#### **2. The principle of the antiresonant reflecting optical waveguide**

The antiresonance reflection principle refers to light that does not meet the resonance condition and is confined to the low refractive index (RI) fiber core for transmission [5]. In 1986, the antiresonant reflecting optical waveguide (ARROW) was proposed by Duguya et al. [5]. The working principle of the ARROW is to use the design of the multilayer high reflection film between the waveguide and silicon substrate (most of which use the double-layer film) to transmit the light beam in the waveguide layer, so as to reduce the energy leakage, with the characteristics of single mode and small loss [5, 6, 16]. The ARROW structure is a promising waveguide structure for silicon-based sensors and has been used for a variety of purposes because it allows the thickness of the buffer layer to be reduced and the single-mode size to be increased and the process tolerance and material selection range to be relatively expanded [17–19].

*The Antiresonant Reflecting Optical Waveguide Fiber Sensor DOI: http://dx.doi.org/10.5772/intechopen.93345*

**Figure 1.** *The structure of ARROW.*

The ARROW can be used to study the optical conduction mechanism of lowindex core fibers, which is similar to Fabry-Pérot resonators [6]. **Figure 1** shows the structure diagram of the ARROW, where the gray part is the high-index layer with RI n2 (silica) corresponding to the Fabry-Pérot resonator cavity and the dark gray part is the low-index layer with RI n1 (air) [17, 18]. When the wavelength of the optical fiber satisfies the resonance condition, it will leak out from the high fold rate layer corresponding to the low transmission intensity part of the transmission spectrum, which is similar to the destructive interference of light in the Fabry-Pérot cavity [19, 20]. In contrast, the light of the antiresonance wavelength will be reflected back at the interface of the high and low RIs and will be restricted to be transmitted in the fiber core. So most of the light will be reflected back to the fiber core [20]. Based on the principle of the antiresonant waveguide, the optical fiber sensor can be made into different types by changing the relevant parameters. Optical fiber sensors based on the antiresonant waveguide are mainly divided into two types [21]. The first is to change the resonant wavelength by changing the RI or the length of the Fabry-Pérot cavity. The second is to change the contrast of the output intensity of the antiresonant waveguide by changing the associated external material composition [19, 20]. The optical fiber sensor of the ARROW finally realizes the measurement of different physical quantities through these two kinds of modulation methods. This chapter will introduce the working principles of various ARROW-based fiber optic sensors in detail [20, 21].

### **3. The antiresonant reflecting optical waveguide sensor**

#### **3.1 The single-layered antiresonant reflecting optical waveguide sensor**

The simplest model of the antiresonant reflecting optical waveguide (ARROW) is the single-layered antiresonant reflecting optical waveguide (SL-ARROW), which is widely used in optical fiber sensors. The SL-ARROW mode in the capillary waveguide is sensitive to the surrounding environments, and various sensing applications have been proposed, such as vibration sensor, humidity sensor, water-level sensing, etc. The working principle of the SL-ARROW is introduced by the vibration sensor [7].

Vibration signal detection is very important in the application of structural monitoring in people's life. Vibration detection can monitor the safety of building structures such as buildings, highways, bridges, dams, highways, and so on. In general, the vibration can be detected by piezoelectric, magneto-electric, and current sensors [22]. SL-ARROW is an optical fiber vibration sensor, which is designed based on the principle of antiresonant waveguide. The fiber optic sensor is a good alternative with several unique advantages such as low weight, immunity to electromagnetic interference, and long-distance signal transmission for remote

applications [5, 6]. The optical fiber sensor based on the principle of ARROW is mainly applied in the optical fiber vibration sensor, optical fiber humidity sensor, water-level sensor, fiber strain sensor, fiber optic magnetic field sensor, fiber optic biosensors, optical fiber pressure sensor, optical fiber temperature sensor, and other types of optical fiber sensors. The common optical fiber sensors based on the

**2. The principle of the antiresonant reflecting optical waveguide**

The antiresonance reflection principle refers to light that does not meet the resonance condition and is confined to the low refractive index (RI) fiber core for transmission [5]. In 1986, the antiresonant reflecting optical waveguide (ARROW) was proposed by Duguya et al. [5]. The working principle of the ARROW is to use the design of the multilayer high reflection film between the waveguide and silicon substrate (most of which use the double-layer film) to transmit the light beam in the waveguide layer, so as to reduce the energy leakage, with the characteristics of single mode and small loss [5, 6, 16]. The ARROW structure is a promising waveguide structure for silicon-based sensors and has been used for a variety of purposes because it allows the thickness of the buffer layer to be reduced and the single-mode size to be increased and the process tolerance and material selection range to be

ARROW principle and their performance are shown in **Table 1**.

**Sensors Performance Application**

*Electromagnetic Propagation and Waveguides in Photonics and Microwave Engineering*

(1) Signal-to-noise ratio of 60 dB, (2) wide frequency response from 5 to 10 kHz, and (3) high sensitivity and low temperature

(1) The sensitivity of up to 0.22 dB/% RH and (2) good repeatability, fast response time, and low temperature cross-

(1) Magnetic field sensitivity of 81 pm/Oe and (2) low temperature cross-sensitivity

(1) The limit of detection of 0.5 ng/ml can be achieved for the IFN-γ concentration and (2) the influence of the temperature could be compensated through the referenced resonance dip

(1) The pressure sensitivity of 4.42 nm/ MPa and (2) the spatial sensitivity of 0.86 nm/cm can be achieved

Applications for the monitoring of smart structures such as buildings, bridges, highways, pavements, dams, and so on

Applications for human daily biology, industrial production, agriculture, animal

Applications for industrial production, motor, and electronic products' magnetic

Applications for health monitoring, cancer prevention, biological engineering, etc.

Applications for multipoint pressure detection in the fields of security, structure monitoring, and oil exploration

production, space exploration, and other

husbandry, and other fields

Applications for the accurate measurement of the strain of smart

Sensitivity of 1.1 dB/mm Applications for water-level monitoring

Temperature sensitivity of 70.71 pm/°C Applications for biomedicine, industrial

fields

structures

field measurement

cross-sensitivity

Strain sensor (1) The resolution of the sensor is 27.9 pm/ με and (2) the temperature crosssensitivity is only 1.67 pm/°C

sensitivity

*The optical fiber sensor based on ARROW [7–15].*

Vibration sensor

Humidity sensor

Water-level sensor

Magnetic field sensor

Optic biosensors

Pressure sensor

**Table 1.**

Temperature sensor

relatively expanded [17–19].

**12**

operation [23]. Here, an all-fiber vibration sensor based on the SL-ARROW has been proposed in a tapered capillary fiber. The schematic construction of the proposed vibration sensor is given in **Figure 2**. In order to fabricate the sensor, the capillary optical fiber is selected as the sensing fiber. The capillary fiber consists of a hollow core with an inner diameter of 30 μm and a ring-cladding with a thickness of 55 μm. Both ends of the 8 cm long capillary optical fiber are cut by the highprecision cutter, and the cut capillary fiber and single-mode fiber (SMF) are spliced through the fiber splicer. The cross section of the capillary fiber and the splicing diagram between the capillary fiber and SMF are shown in **Figure 2** [7].

cladding to generate the transmission spectrum. In the transmission spectrum, periodic and narrow loss attenuation corresponding to the Fabry-Pérot cavity resonance condition will appear [7]. The wavelength of the lossy dip corresponding to the

*<sup>λ</sup><sup>r</sup>* <sup>¼</sup> <sup>2</sup>*<sup>d</sup>* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

where *n* and *n*<sup>0</sup> are the RIs of the capillary fiber cladding and air, respectively, *d* is the thickness of capillary fiber cladding, and *m* is the resonance order [7]. The mechanical analysis of the photoelastic effect of the tapered region under

ð Þ 1 þ *γ* ð Þ *P*<sup>12</sup> � *P*<sup>11</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>4</sup> *n*<sup>2</sup>ð Þ 1 þ *γ* ð Þ *P*<sup>12</sup> � *P*<sup>11</sup>

*m*

*The frequency spectrum of the tapered capillary fiber corresponding to (a) 5 Hz, (b) 10 Hz, (c) 1 kHz, and*

� �<sup>2</sup> � �<sup>2</sup>

where Δ*n* is the change of the RI, *n* is the RI of the silica, *P*<sup>11</sup> and *P*<sup>12</sup> are the optoelastic constants of silica, *γ* is the Poisson ratio of silica, *A* is the diameter of the tapered region, and *R* is the bending radius. Substitution of Eq. (1) into Eq. (2) gives

*A R* � �<sup>2</sup>

> *A R*

� *n*<sup>2</sup> 0

p *m*

*n*<sup>2</sup> � *n*<sup>2</sup> 0

(1)

(2)

(3)

resonance condition *λ<sup>r</sup>* can be expressed as Eq. (1) [7, 22]:

*The Antiresonant Reflecting Optical Waveguide Fiber Sensor*

*DOI: http://dx.doi.org/10.5772/intechopen.93345*

<sup>Δ</sup>*<sup>n</sup>* <sup>¼</sup> <sup>1</sup> 4 *n*2

*<sup>n</sup>* <sup>þ</sup> <sup>1</sup>

bending can be expressed as follows [7]:

*λ<sup>r</sup>* ¼

**Figure 4.**

**15**

*(d) 10 kHz [25].*

2ð*d*

r

The principle of using capillary fiber to make vibration sensor can be described as an SL-ARROW [24]. As the RI of the cladding is larger than that of the core, the core mode can oscillate and radiate through the cladding. The cladding modes propagate in the cladding region of the capillary fiber, as shown in **Figure 3(a)**. The working principle of the tapered capillary fiber can be approximated to Fabry-Pérot etalon, as shown in **Figure 3(b)**. When the wavelengths cannot satisfy the resonant condition, the optical waveguide will be confined in the hollow core of the fiber as the core modes. Therefore, the guide light can be reflected by the resonator. On the contrary, when the wavelength meets the resonant condition, the guided light will resonate and will not be reflected by the Fabry-Pérot cavity and will leak out of the

**Figure 2.**

*The schematic construction of the proposed sensor [7].*

#### **Figure 3.**

*(a) Schematic diagram of the cross section of the capillary fiber and (b) the guiding mechanism of the capillary fiber [7].*

operation [23]. Here, an all-fiber vibration sensor based on the SL-ARROW has been proposed in a tapered capillary fiber. The schematic construction of the proposed vibration sensor is given in **Figure 2**. In order to fabricate the sensor, the capillary optical fiber is selected as the sensing fiber. The capillary fiber consists of a hollow core with an inner diameter of 30 μm and a ring-cladding with a thickness of 55 μm. Both ends of the 8 cm long capillary optical fiber are cut by the highprecision cutter, and the cut capillary fiber and single-mode fiber (SMF) are spliced through the fiber splicer. The cross section of the capillary fiber and the splicing

*Electromagnetic Propagation and Waveguides in Photonics and Microwave Engineering*

diagram between the capillary fiber and SMF are shown in **Figure 2** [7].

**Figure 2.**

**Figure 3.**

*fiber [7].*

**14**

*The schematic construction of the proposed sensor [7].*

The principle of using capillary fiber to make vibration sensor can be described as an SL-ARROW [24]. As the RI of the cladding is larger than that of the core, the core mode can oscillate and radiate through the cladding. The cladding modes propagate in the cladding region of the capillary fiber, as shown in **Figure 3(a)**. The working principle of the tapered capillary fiber can be approximated to Fabry-Pérot etalon, as shown in **Figure 3(b)**. When the wavelengths cannot satisfy the resonant condition, the optical waveguide will be confined in the hollow core of the fiber as the core modes. Therefore, the guide light can be reflected by the resonator. On the contrary, when the wavelength meets the resonant condition, the guided light will resonate and will not be reflected by the Fabry-Pérot cavity and will leak out of the

*(a) Schematic diagram of the cross section of the capillary fiber and (b) the guiding mechanism of the capillary*

cladding to generate the transmission spectrum. In the transmission spectrum, periodic and narrow loss attenuation corresponding to the Fabry-Pérot cavity resonance condition will appear [7]. The wavelength of the lossy dip corresponding to the resonance condition *λ<sup>r</sup>* can be expressed as Eq. (1) [7, 22]:

$$
\lambda\_r = \frac{2d\sqrt{n^2 - n\_0^2}}{m} \tag{1}
$$

where *n* and *n*<sup>0</sup> are the RIs of the capillary fiber cladding and air, respectively, *d* is the thickness of capillary fiber cladding, and *m* is the resonance order [7].

The mechanical analysis of the photoelastic effect of the tapered region under bending can be expressed as follows [7]:

$$
\Delta n = \frac{1}{4}n^2(1+\gamma)(P\_{12} - P\_{11})\left(\frac{A}{R}\right)^2\tag{2}
$$

where Δ*n* is the change of the RI, *n* is the RI of the silica, *P*<sup>11</sup> and *P*<sup>12</sup> are the optoelastic constants of silica, *γ* is the Poisson ratio of silica, *A* is the diameter of the tapered region, and *R* is the bending radius. Substitution of Eq. (1) into Eq. (2) gives

$$\lambda\_r = \frac{2(d\sqrt{\left(n + \frac{1}{4}n^2(1+\chi)(P\_{12} - P\_{11})\left(\frac{A}{R}\right)^2\right)^2 - n\_0^2}}{m} \tag{3}$$

#### **Figure 4.**

*The frequency spectrum of the tapered capillary fiber corresponding to (a) 5 Hz, (b) 10 Hz, (c) 1 kHz, and (d) 10 kHz [25].*

According to Eq. (3), it can be seen that the wavelength of the loss dip in the transmission spectrum under resonance condition is highly sensitive to the small change of bending radius in the tapered region. This provides an attractive method for vibration detection.

To test the frequency response of the fiber vibration sensor, the corresponding frequency response experiments were performed, and the transmission spectra are shown in **Figure 4** [7]. In the fiber vibration sensor experiment, the piezoelectric plate was used as the vibration source, which was driven by 1.8 V sinusoidal signals of 5.0 Hz, 10.0 Hz, 1.0 kHz, and 10.0 kHz, respectively. The transmission intensity of the fiber sensor was converted into a frequency spectrum by fast Fourier transform (FFT), as shown in **Figure 4(a)–(d)** [7]. The corresponding time domain signals are shown in the insets. The sampling rate of each frequency is 1 M and the total sampling time is 5 s. All of transmission intensities of sensor were modulated to sinusoidal waveforms with very uniform amplitude [7]. The main peaks of the frequency spectrum are located at 4.98, 9.98, 998.03, and 9998.96 Hz, respectively, which are close to the corresponding driving frequency [25].

#### **3.2 The double-layered antiresonant reflecting optical waveguide**

Compared with the SL-ARROW, the Fabry-Pérot resonator in the ARROW can be also formed through two layers with different claddings of the fiber. A doublelayered Fabry-Pérot resonator can be formed between the silica cladding and polymethyl methacrylate (PMMA) cladding [9, 10]. The DL-ARROW possesses high flexibility, which can be used in various sensing applications such as strain sensor, film sensing, temperature, vibration sensing, etc. Taking the temperature sensor as an example, the working principle of the double-layered ARROW (DL-ARROW) is introduced [9].

In real life, optical fiber temperature sensor has been widely used in temperature measurement in different application areas. Optical fiber temperature sensor has many unique advantages such as immunity to electromagnetic interferences, high sensitivity, repeatability, stability, durability, high resolution and fast response, durability against harsh environments, and other advantages [26]. A temperature sensor based on the DL-ARROW was presented [9]. The cross-sectional view of the fiber is given in **Figure 5 (a)**. A section of the simplified hollow-core (SHC) photonic crystal fiber (PCF) was cleaved at both ends, and one end of the fiber was sealed with glue, as can be seen in **Figure 5(b)**, the selectively opened air hole can be seen in **Figure 5(c)**, and the schematic construction of the proposed device is given in **Figure 5(d)** [9].

The essence of the optical fiber temperature sensor guidance is mainly driven by the silicon rod around the hollow core, which plays the role of the ARROW [25]. Before the fiber is penetrated by alcohol, due to the weak interaction between the core and the cladding mode, light is well restricted in the air core of the SHC-PCF. This can be interpreted as a strong lateral field mismatch between the modes, resulting in the overlap with the core field distribution being washed away. **Figure 6** gives the sketch of the optical path of the beams at the alcohol-filled area and the outer silica cladding [9].

In the presence of alcohol in the SHC-PCF cavity, due to the better phase matching, the interaction between the core layer and the cladding mode can be greatly enhanced, resulting in the degradation of the optical field constraints in the hollow core. The core mode field will radiate through the silicone ring around the air core to the outer cladding. The alcohol-filled cavity combined with the external silicon cladding can be regarded as a double-layer Fabry-Pérot resonant cavity

[9, 27]. For wavelengths that satisfy the resonance conditions of the resonator, constructive interference occurs, which means that the Fabry-Pérot resonator is highly transparent to these wavelengths, and light cannot be reflected and will leak out of the cladding [27]. In contrast, for the antiresonance wavelength (i.e., the

*The optical path of the interference beams at the alcohol-filled area and the outer cladding [10].*

*(a) The cross-sectional view of the SHC-PCF, (b) the SHC-PCF sealed at the end face, (c) with end face sealed*

*selectively opened, and (d) the structure diagram of the sensor.*

*The Antiresonant Reflecting Optical Waveguide Fiber Sensor*

*DOI: http://dx.doi.org/10.5772/intechopen.93345*

**Figure 5.**

**Figure 6.**

**17**

#### **Figure 5.**

According to Eq. (3), it can be seen that the wavelength of the loss dip in the transmission spectrum under resonance condition is highly sensitive to the small change of bending radius in the tapered region. This provides an attractive method

*Electromagnetic Propagation and Waveguides in Photonics and Microwave Engineering*

To test the frequency response of the fiber vibration sensor, the corresponding frequency response experiments were performed, and the transmission spectra are shown in **Figure 4** [7]. In the fiber vibration sensor experiment, the piezoelectric plate was used as the vibration source, which was driven by 1.8 V sinusoidal signals of 5.0 Hz, 10.0 Hz, 1.0 kHz, and 10.0 kHz, respectively. The transmission intensity of the fiber sensor was converted into a frequency spectrum by fast Fourier transform (FFT), as shown in **Figure 4(a)–(d)** [7]. The corresponding time domain signals are shown in the insets. The sampling rate of each frequency is 1 M and the total sampling time is 5 s. All of transmission intensities of sensor were modulated to sinusoidal waveforms with very uniform amplitude [7]. The main peaks of the frequency spectrum are located at 4.98, 9.98, 998.03, and 9998.96 Hz, respectively,

Compared with the SL-ARROW, the Fabry-Pérot resonator in the ARROW can be also formed through two layers with different claddings of the fiber. A doublelayered Fabry-Pérot resonator can be formed between the silica cladding and polymethyl methacrylate (PMMA) cladding [9, 10]. The DL-ARROW possesses high flexibility, which can be used in various sensing applications such as strain sensor, film sensing, temperature, vibration sensing, etc. Taking the temperature sensor as an example, the working principle of the double-layered ARROW

In real life, optical fiber temperature sensor has been widely used in temperature measurement in different application areas. Optical fiber temperature sensor has many unique advantages such as immunity to electromagnetic interferences, high sensitivity, repeatability, stability, durability, high resolution and fast response, durability against harsh environments, and other advantages [26]. A temperature sensor based on the DL-ARROW was presented [9]. The cross-sectional view of the fiber is given in **Figure 5 (a)**. A section of the simplified hollow-core (SHC) photonic crystal fiber (PCF) was cleaved at both ends, and one end of the fiber was sealed with glue, as can be seen in **Figure 5(b)**, the selectively opened air hole can be seen in **Figure 5(c)**, and the schematic construction of the proposed device is

The essence of the optical fiber temperature sensor guidance is mainly driven by the silicon rod around the hollow core, which plays the role of the ARROW [25]. Before the fiber is penetrated by alcohol, due to the weak interaction between the core and the cladding mode, light is well restricted in the air core of the SHC-PCF. This can be interpreted as a strong lateral field mismatch between the modes, resulting in the overlap with the core field distribution being washed away. **Figure 6** gives the sketch of the optical path of the beams at the alcohol-filled area

In the presence of alcohol in the SHC-PCF cavity, due to the better phase matching, the interaction between the core layer and the cladding mode can be greatly enhanced, resulting in the degradation of the optical field constraints in the hollow core. The core mode field will radiate through the silicone ring around the air core to the outer cladding. The alcohol-filled cavity combined with the external silicon cladding can be regarded as a double-layer Fabry-Pérot resonant cavity

which are close to the corresponding driving frequency [25].

**3.2 The double-layered antiresonant reflecting optical waveguide**

for vibration detection.

(DL-ARROW) is introduced [9].

given in **Figure 5(d)** [9].

and the outer silica cladding [9].

**16**

*(a) The cross-sectional view of the SHC-PCF, (b) the SHC-PCF sealed at the end face, (c) with end face sealed selectively opened, and (d) the structure diagram of the sensor.*

*The optical path of the interference beams at the alcohol-filled area and the outer cladding [10].*

[9, 27]. For wavelengths that satisfy the resonance conditions of the resonator, constructive interference occurs, which means that the Fabry-Pérot resonator is highly transparent to these wavelengths, and light cannot be reflected and will leak out of the cladding [27]. In contrast, for the antiresonance wavelength (i.e., the

wavelength that does not satisfy the resonance condition), destructive interference occurs, and light can be well reflected by the Fabry-Pérot resonator [9]. The Fabry-Pérot resonator is confined within the cavity of the optical fiber and serves as a guide for the waveguide mold. The position of the non-transmitted wavelength can be described by the following formula as Eq. (4) [9, 27]:

$$\lambda\_m = \frac{2(d\_1\sqrt{n\_1^2 - n\_0^2} + d\_2\sqrt{n\_2^2 - n\_0^2})}{m} \tag{4}$$

**3.3 The double resonator antiresonant reflecting optical waveguide sensor**

ple of the DR-ARROW is introduced [12].

*The Antiresonant Reflecting Optical Waveguide Fiber Sensor*

*DOI: http://dx.doi.org/10.5772/intechopen.93345*

**Figure 8.**

**19**

*of the dual-optofluidic waveguide ARROW [12].*

Both the SL-ARROW and DL-ARROW are formed to generate the ARROW effect in the fiber optic sensor. However, many long-standing challenges still exist in the ARROW-based fiber sensor, such as serious temperature cross-sensitivity [12]. The ambient temperature change can also modulate the resonance condition of ARROW, making a decrease of the measurement accuracy for both SL-ARROW and DL-ARROW. Therefore, the double resonator ARROW (DR-ARROW) has been investigated to solve the temperature cross talk in the fiber sensor. In this section, the biosensor fiber sensors are taken as examples, and the working princi-

The in-line fiber optofluidic waveguide biosensors possess both enhanced sensing performance and ultracompact size, which have been widely used in the lab-infibers chemical and biological sensing [12]. In-line fiber biosensors possess many distinctive advantages such as high sensitivity, compact size, and immunity to electromagnetic interference [28]. Here, a biosensor based on DR-ARROW for the detection of interferon-gamma (IFN-γ) concentration has been introduced. The schematic construction of the proposed biosensor sensor is given in **Figure 8**. In the proposed sensor, a HCF was employed as the sensing fiber, as shown in **Figure 8(a)**. The HCF consists of an air octagon core, an air-ring cladding with eight holes, and a silica cladding. The NaCl solution was filled into a cladding hole with a length of 10 cm through the capillary force by immersing the remaining SMF into the NaCl

*(a) The cross section of the HCF. (b) The cross-section of the NaCl-infiltrated HCF. (c) The schematic diagram*

where *d*<sup>1</sup> is the thickness of the air cladding, *d*<sup>2</sup> is the thickness of the outer cladding, and *m* is a positive integer. *n*0, *n*<sup>1</sup> and *n*<sup>2</sup> are the refractive indices of air, alcohol and silica, respectively. From Eq. (4), it can be seen that the resonant wavelengths are mainly determined by the thickness of the alcohol and the outer silicon cladding and the material index.

By differentiating Eq. (4) with respect to temperature (T), we get the temperature sensitivity as in Eq. (5). It should be noted that in Eq. (5), we only considered the change of *n*<sup>1</sup> (*dn*<sup>1</sup> ¼ *αdT*, *α* is the thermo-optic coefficient of alcohol), since silica has a much smaller thermo-optic coefficient than alcohol, which can be ignored in this case as Eq. (5) [9]:

$$\frac{\partial \lambda\_m}{\partial T} = \frac{2d\_1 n\_1}{m\sqrt{n\_1^2 - n\_0^2}} a \tag{5}$$

The thermo-optic coefficient of alcohol is �3.99 � <sup>10</sup>�<sup>4</sup> .

The temperature response characteristics of this temperature sensor were investigated in a temperature box with adjustable temperature. The temperature sensor with a filling length of 1.2 cm is put into a temperature box. The temperature of the temperature box was heated from room temperature to 60° with an increment of 10°C. The maximum value of temperature measurement is limited below the boiling point of alcohol (78.37°) [9]. This situation can be improved by using a liquid with higher boiling point like ethylene glycol [9]. The attenuation dips were found to shift toward shorter wavelengths with temperature increasing, as can be seen in **Figure 7(a)** [9]. The wavelength shift versus temperature in the experiment is plotted in **Figure 7(b)**, and the temperature sensitivity was obtained to be �0.48 nm/°. [9].

**Figure 7.**

*(a) Spectrum blueshift with increasing of temperature and (b) temperature response of the SHC-PCF with filling length of 2 cm [9].*

wavelength that does not satisfy the resonance condition), destructive interference occurs, and light can be well reflected by the Fabry-Pérot resonator [9]. The Fabry-Pérot resonator is confined within the cavity of the optical fiber and serves as a guide for the waveguide mold. The position of the non-transmitted wavelength can

*Electromagnetic Propagation and Waveguides in Photonics and Microwave Engineering*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *n*2 <sup>1</sup> � *<sup>n</sup>*<sup>2</sup> 0 <sup>p</sup> <sup>þ</sup> *<sup>d</sup>*<sup>2</sup>

where *d*<sup>1</sup> is the thickness of the air cladding, *d*<sup>2</sup> is the thickness of the outer cladding, and *m* is a positive integer. *n*0, *n*<sup>1</sup> and *n*<sup>2</sup> are the refractive indices of air, alcohol and silica, respectively. From Eq. (4), it can be seen that the resonant wavelengths are mainly determined by the thickness of the alcohol and the outer

By differentiating Eq. (4) with respect to temperature (T), we get the temperature sensitivity as in Eq. (5). It should be noted that in Eq. (5), we only considered the change of *n*<sup>1</sup> (*dn*<sup>1</sup> ¼ *αdT*, *α* is the thermo-optic coefficient of alcohol), since silica has a much smaller thermo-optic coefficient than alcohol, which can be

*m*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *n*2 <sup>2</sup> � *<sup>n</sup>*<sup>2</sup> 0

<sup>p</sup> *<sup>α</sup>* (5)

.

(4)

p

be described by the following formula as Eq. (4) [9, 27]:

*<sup>λ</sup><sup>m</sup>* <sup>¼</sup> <sup>2</sup>ð*d*<sup>1</sup>

*∂λ<sup>m</sup>*

The thermo-optic coefficient of alcohol is �3.99 � <sup>10</sup>�<sup>4</sup>

*<sup>∂</sup><sup>T</sup>* <sup>¼</sup> <sup>2</sup>*d*1*n*<sup>1</sup>

*(a) Spectrum blueshift with increasing of temperature and (b) temperature response of the SHC-PCF with*

*m* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *n*2 <sup>1</sup> � *n*<sup>2</sup> 0

The temperature response characteristics of this temperature sensor were investigated in a temperature box with adjustable temperature. The temperature sensor with a filling length of 1.2 cm is put into a temperature box. The temperature of the temperature box was heated from room temperature to 60° with an increment of 10°C. The maximum value of temperature measurement is limited below the boiling point of alcohol (78.37°) [9]. This situation can be improved by using a liquid with higher boiling point like ethylene glycol [9]. The attenuation dips were found to shift toward shorter wavelengths with temperature increasing, as can be seen in **Figure 7(a)** [9]. The wavelength shift versus temperature in the experiment is plotted in **Figure 7(b)**, and the temperature sensitivity was obtained to be

silicon cladding and the material index.

ignored in this case as Eq. (5) [9]:

�0.48 nm/°. [9].

**Figure 7.**

**18**

*filling length of 2 cm [9].*
